Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Schipper, Pieter E.; Gritsenko, O. V.; Baerends, Evert Jan

doi:10.1007/s002140050273

Cited by 85 publications

(87 citation statements)

References 28 publications

(38 reference statements)

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“…[18]. Our analysis started with the observation [6] that GGA potentials, or the asymptotically correct (behaving as 21͞r for large r) LB94 xc potential [19], do not improve upon LDA (thus showing that the problem is unrelated to the slight LDA overestimation for small molecules [20]).…”

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confidence: 99%

Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains

et al. 1999

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Density functional calculations on the (non)linear optical properties of conjugated molecular chains using currently popular exchange-correlation (xc) potentials give overestimations of several orders of magnitude. By analyzing "exact" and Krieger-Li-Iafrate xc potentials, the error is traced back to an incorrect electric field dependence of the "response part" of the xc potential in local and gradientcorrected density approximations, which lack a linear term counteracting the applied electric field.PACS numbers: 31.15. Ew, 42.65.An, 71.15.Mb, 77.22.Ej The nonlinear optical (NLO) properties of molecules are of considerable current interest, both from the fundamental and technological points of view [1][2][3]. Prototype systems exhibiting large NLO responses like the polyacetylene (PA) chains have been studied intensively with conventional, ab initio Hartree-Fock (HF) based theoretical techniques [2]. Because density functional theory (DFT) [4,5] usually provides clearly improved accuracy with respect to HF at similar or lower computational cost, it seems tempting to apply DFT to the prediction of the NLO properties of large, conjugated molecular chains.Our calculations on static hyperpolarizabilities (determining the NLO response in the static limit) of such chains show, both here and in Ref. [6], that the local density approximation (LDA) and generalized gradient approximations (GGAs) in DFT provide very poor results. Whereas previously reported LDA errors are typically 10% for dielectric constants, we find overestimations of several orders of magnitude for the second hyperpolarizability g. In view of the respectable accuracy which is usually obtained in DFT calculations, this is highly surprising and deserves a detailed analysis, as this error may be among the largest in the history of DFT calculations. Our analysis allows us to pinpoint the weakness of the LDA. It will be shown below that, if an electric field, E, is applied, the so-called response part of the exact exchange-correlation (xc) potential develops a global behavior counteracting the applied field. Such behavior is not present in the LDA or GGA potentials. Our results substantiate and further elucidate the findings of Gonze, Ghosez, and Godby [7] and others [8][9][10][11][12][13], who pointed out the existence of such a counteracting linear potential in the exact y xc and provided the first physical interpretation for it [10,13].Description of the problem.-For this work, extensive calculations have been performed on PA and hydrogen chains. The LDA results described below have been obtained in the same manner as earlier calculations on the polarizability (a) and second hyperpolarizability (g) of C 60 [14]. Details of the computational procedure, the geometries, etc., have been given in another paper [6], where several aspects of the LDA problem (size of electron correlation correction, effect of bond length alternation) are described more fully.From the HF-based ab initio studies [15] on the NLO properties of PA chains, it is known that even sim...

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Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains

et al. 1999

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“…These numerical potentials features considerable oscillations which are most pronounced near the nucleus. Such an oscillatory behavior is commonly found when the target density is expanded in GTOs 84 and can be attributed to their deficiency to represent the correct form of the electron density close to the nucleus. However, these oscillations can be reduced when the GTO orbital basis set used for determining the target density is enlarged (see Fig.…”

Section: Full-ci Target (Spin) Density Expanded In Gtosmentioning

confidence: 99%

“…Most likely, these can be attributed to the deficiencies of the GTO target density, which can cause such oscillations in the exact potentials. 84 To compare the overall performance of the different potential reconstruction schemes, Fig. 8 compares the optimal and the smooth spin potentials in the xy-plane.…”

Section: Casscf (Spin) Density Expanded In Gtosmentioning

confidence: 99%

Optimized unrestricted Kohn–Sham potentials from ab initio spin densities

Boguslawski

Jacob

Reiher

2013

The Journal of Chemical Physics

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The reconstruction of the exchange-correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For openshell systems, the spin density is introduced as an additional fundamental variable in spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn-Sham (KS) potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange-correlation potential, which determines the spin density in unrestricted KS-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [Ch. R. Jacob, J. Chem. Phys. 135, 244102 (2011)] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from full configuration interaction and complete active space self-consistent field calculations, respectively.

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“…An analysis by Schipper et al [4] of the H 2 + H 2 reaction is a beautiful illustration. These authors have computed accurate CI and MRCI wavefunctions at various points on the H 2 + H 2 potential-energy surface and, at each geometry, have extracted the exact Kohn-Sham potential v KS and orbitals ψ i using a robust Kohn-Sham inversion procedure [5]. For geometries close to perfect squares (D 4h ), their inversion procedure fails to converge; i.e., occupation "holes" appear under the HOMO if single-determinant occupancies are enforced.…”

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confidence: 99%

Fractional Kohn–Sham Occupancies from a Strong-Correlation Density Functional

Becke

2014

Topics in Current Chemistry

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It is not always possible in Kohn-Sham density-functional theory for the non-interacting reference state to have integer-only occupancies. Cases of "strong" correlation, with very small HOMO-LUMO gaps, involve fractional occupancies. At the transition states of symmetric avoided-crossing reactions, for example, representation of the correct density requires a 50/50 mixing of degenerate HOMOs. In a recent paper (Becke, J Chem Phys 139:021104, 2013) the "B13" strong-correlation density functional of Becke (J Chem Phys 138:074109, 2013 and 138:161101, 2013) was shown to give excellent barrier heights in symmetric avoided-crossing reactions. However, the calculations were performed only at reactant and transition-state geometries, where the fractional HOMO-LUMO occupancies in the latter are 50/50 by symmetry. In the present chapter, we compute full reaction curves for avoided crossings in H 2 + H 2 , ethylene (twisting around the double bond), and cyclobutadiene (double-bond automerization) by determining fractional occupancies variationally. We adopt a practical strategy for doing so which does not involve self-consistent B13 computations (not yet possible) and involves minimal cost. Single-bond dissociation curves for H 2 and LiH are also presented.

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Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

Cited by 85 publications

References 28 publications

Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains

Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains

Optimized unrestricted Kohn–Sham potentials from ab initio spin densities

Fractional Kohn–Sham Occupancies from a Strong-Correlation Density Functional

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